Polydispersity in curved polymer brushes, in the strong-stretching limit

Polymer brushes are nanostructures characterised by dense polymer brushes tethered onto a surface, resembling real-life brushes. In the past, polymer brushes have been investigated theoretically either in the monodisperse limit or in flat geometries. These circumstances however aren’t as experimentally relevant, as monodisperse brushes are difficult to construct and brushes are found in curved geometries most of the times.

Here, we attempt to resolve this issue by extending the already established mean-field theory describing polymer brushes developed by Cates et.al. .We develop a theory that allows us to investigate for arbitrary geometries and polydispersities. We then explore the uniform, Schulz-Zimm and monodisperse polymer distributions, and note the emergence of an End Exclusion Zone in convex geometries and we note the conditions that give rise to it.